Details

sample118.0ms

Algorithm

intervals

Results

31.0ms	64×	body	10240	exit
30.0ms	51×	body	1280	valid
16.0ms	51×	body	640	valid
6.0ms	110×	body	80	valid
6.0ms	4×	body	2560	valid
5.0ms	28×	body	320	valid
3.0ms	95×	body	80	nan
1.0ms	7×	body	640	nan
1.0ms	12×	body	160	valid
1.0ms	6×	body	320	nan
0.0ms	2×	body	160	nan

simplify20.3s

Counts

1 → 1

Iterations

Useful iterations: 8 (170.0ms)

Iter	Nodes	Cost
0	12	13
1	20	13
2	35	12
3	51	12
4	78	12
5	134	12
6	204	12
7	288	12
8	477	10
9	719	10
10	885	10
11	934	10
12	1264	10
13	3672	10
done	5000	10

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.2b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(- x (/ (log (fma (expm1 z) y 1.0)) t))
0.1b	(/ (log (fma (expm1 z) y 1.0)) t)
3.8b	(log (fma (expm1 z) y 1.0))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
56×	`*-un-lft-identity`
54×	`add-cube-cbrt`
49×	`times-frac`
48×	`prod-diff`
17×	`pow1`
14×	`log-pow`
6×	`add-exp-log`
5×	`add-cbrt-cube` `add-log-exp`
4×	`div-inv` `associate-/l*`
3×	`expm1-log1p-u` `log-prod` `fma-neg` `associate-/r*` `log1p-expm1-u`
2×	`difference-of-squares`
1×	`cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `clear-num` `flip--` `distribute-lft-out--`

Counts

3 → 115

Calls

3 calls:

9.0ms	(- x (/ (log (fma (expm1 z) y 1.0)) t))
3.0ms	(/ (log (fma (expm1 z) y 1.0)) t)
1.0ms	(log (fma (expm1 z) y 1.0))

series262.0ms

Counts

3 → 9

Calls

3 calls:

71.0ms	(- x (/ (log (fma (expm1 z) y 1.0)) t))
125.0ms	(/ (log (fma (expm1 z) y 1.0)) t)
65.0ms	(log (fma (expm1 z) y 1.0))

simplify789.0ms

Counts

124 → 124

Iterations

Useful iterations: done (784.0ms)

Iter	Nodes	Cost
0	252	4198
1	601	3760
2	2009	2551
done	5000	2542

prune307.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(- x (/ 1 (/ t (log (fma (expm1 z) y 1.0)))))
0.1b	(/ 1 (/ t (log (fma (expm1 z) y 1.0))))
0.1b	(/ t (log (fma (expm1 z) y 1.0)))
3.8b	(log (fma (expm1 z) y 1.0))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

366×	`times-frac`
254×	`add-sqr-sqrt`
245×	`*-un-lft-identity`
240×	`add-cube-cbrt`
159×	`prod-diff`
49×	`pow1`
44×	`log-pow`
20×	`associate-/r*`
19×	`div-inv`
18×	`add-exp-log`
11×	`add-cbrt-cube`
8×	`div-exp`
6×	`associate-/l*` `add-log-exp`
5×	`difference-of-squares`
4×	`cbrt-undiv` `expm1-log1p-u` `associate-/r/` `log1p-expm1-u`
3×	`log-prod` `fma-neg`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `distribute-lft-out--`
1×	`sub-neg` `flip3--` `pow-flip` `diff-log` `rem-log-exp` `flip--` `inv-pow`

Counts

4 → 320

Calls

4 calls:

29.0ms	(- x (/ 1 (/ t (log (fma (expm1 z) y 1.0)))))
6.0ms	(/ 1 (/ t (log (fma (expm1 z) y 1.0))))
2.0ms	(/ t (log (fma (expm1 z) y 1.0)))
1.0ms	(log (fma (expm1 z) y 1.0))

series410.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(- x (/ 1 (/ t (log (fma (expm1 z) y 1.0)))))
85.0ms	(/ 1 (/ t (log (fma (expm1 z) y 1.0))))
184.0ms	(/ t (log (fma (expm1 z) y 1.0)))
70.0ms	(log (fma (expm1 z) y 1.0))

simplify549.0ms

Counts

332 → 332

Iterations

Useful iterations: done (529.0ms)

Iter	Nodes	Cost
0	606	16144
1	1570	13910
done	5000	10446

prune588.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (/ (log (fma (expm1 z) y 1.0)) t))
3.8b	(log (fma (expm1 z) y 1.0))
3.8b	(log (fma (expm1 z) y 1.0))
3.8b	(log (fma (expm1 z) y 1.0))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

16×	`cbrt-prod`
15×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac`
10×	`pow1`
9×	`log-prod`
7×	`add-exp-log`
6×	`log-pow`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`rem-log-exp`
1×	`cbrt-div` `pow1/3` `div-inv`

Counts

4 → 69

Calls

4 calls:

2.0ms	(cbrt (/ (log (fma (expm1 z) y 1.0)) t))
1.0ms	(log (fma (expm1 z) y 1.0))
1.0ms	(log (fma (expm1 z) y 1.0))
1.0ms	(log (fma (expm1 z) y 1.0))

series539.0ms

Counts

4 → 12

Calls

4 calls:

337.0ms	(cbrt (/ (log (fma (expm1 z) y 1.0)) t))
68.0ms	(log (fma (expm1 z) y 1.0))
69.0ms	(log (fma (expm1 z) y 1.0))
65.0ms	(log (fma (expm1 z) y 1.0))

simplify476.0ms

Counts

81 → 81

Iterations

Useful iterations: 2 (144.0ms)

Iter	Nodes	Cost
0	197	1445
1	460	1353
2	1610	1229
done	5000	1229

prune468.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.1b

localize24.0ms

Local error

Found 4 expressions with local error:

3.8b	(log (fma (expm1 z) y 1.0))
3.8b	(log (fma (expm1 z) y 1.0))
3.8b	(log (sqrt (fma (expm1 z) y 1.0)))
3.8b	(log (sqrt (fma (expm1 z) y 1.0)))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

18×	`log-prod`
10×	`pow1` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
8×	`add-exp-log` `log-pow`
6×	`sqrt-prod`
4×	`expm1-log1p-u` `rem-log-exp` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`sqrt-pow1` `pow1/2`

Counts

4 → 66

Calls

4 calls:

1.0ms	(log (fma (expm1 z) y 1.0))
1.0ms	(log (fma (expm1 z) y 1.0))
4.0ms	(log (sqrt (fma (expm1 z) y 1.0)))
1.0ms	(log (sqrt (fma (expm1 z) y 1.0)))

series416.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(log (fma (expm1 z) y 1.0))
62.0ms	(log (fma (expm1 z) y 1.0))
148.0ms	(log (sqrt (fma (expm1 z) y 1.0)))
140.0ms	(log (sqrt (fma (expm1 z) y 1.0)))

simplify634.0ms

Counts

78 → 78

Iterations

Useful iterations: done (631.0ms)

Iter	Nodes	Cost
0	198	1718
1	547	1570
2	2193	1434
done	5000	1420

prune500.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.0b

regimes437.0ms

Accuracy

42.4% (4.1b remaining)

Error of 8.5b against oracle of 4.4b and baseline of 11.4b

bsearch50.0ms

Steps

Iters	Range		Point
5	-3.460978998595751e-79	-9.125160771875588e-80	-2.3067511430719193e-79

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	34
1	29	34
done	29	34

end0.0ms

sample3.1s

Algorithm

intervals

Results

757.0ms	1552×	body	10240	exit
755.0ms	1440×	body	1280	valid
453.0ms	1581×	body	640	valid
202.0ms	3486×	body	80	valid
169.0ms	946×	body	320	valid
134.0ms	106×	body	2560	valid
91.0ms	2566×	body	80	nan
53.0ms	459×	body	160	valid
53.0ms	268×	body	640	nan
32.0ms	111×	body	1280	nan
30.0ms	203×	body	320	nan
10.0ms	121×	body	160	nan